Mathematically Modeling Heart In 3D And 4D

The heart, which is the power source of human circulatory system, is one of the most important organs of human bodies. It is such a complex integrated system that includes Physiology, Dynamics, Blood Hydrodynamics and neurological, biochemical control. Modeling is an efficient tool to analyze the complex problems of biology.In this paper, we build 3D static and 4D dynamic models of heart and design visual interface to observe and operate it. The heart models are used on one hand to restrict and instruct coronary artery modeling as a result of coronary artery above the heart interface, the other hand to get 2D images through X-Ray for analyzing angiogram image of coronary artery.In this paper, constructing 3D surfaces of pericardium and antrum is used to model 3D static heart. First we manually segment the slice ups of human heart to get profiles and smooth them by Gaussian filters. Then the uniform sampling algorithm is used to sample points from the profiles. After it, a 3D surface model is constructed from the sampled points applying a surface fitting algorithm. Nonuniform Rational B-Spline (NURBS)is represented to fit surface as its accuracy and manageability. Static heart is the foundation of dynamic heart. After constructing and connecting a series of time frames of static heart models, a dynamic heart model has been constructed. Cardiac circle is divided into 7 time segments based on physiology knowledge and the movement between each segment is supposed linear. In accordance of description of heart movement, 7 time frames are constructed and connected together to form the dynamic heart model.Visual Toolkit (VTK)is used as the visualization tool. It can not only show the static and dynamic heart models, but also handle them freely.The result indicates the static heart model constructed looks like real heart and the dynamic heart model built expresses heart movement well.